Definition

1. Noun:
   • Conditional probability: The probability that a specific event will occur, given that one or more other events have already occurred or are known to have occurred. It measures the likelihood of an event under a specific condition or set of conditions.

Usage

• Noun:
  • This term is used in the fields of statistics, probability theory, and data science to describe a calculated likelihood that depends on prior information.
  • It is a fundamental concept for understanding dependent events and is central to Bayes' theorem.

Examples

• Noun:
  • To predict system failure, engineers calculated the contingent probability of a component failing given that a prior warning signal had been triggered.
  • The study aimed to find the contingent probability of a patient recovering, given that they received the new treatment.

Advanced Usage

• Mathematical Notation: Often denoted as P(A|B), read as "the probability of A given B," where A is the event of interest and B is the known condition.
  • The formula P(Rain|Cloudy) represents the contingent probability of rain given that it is cloudy.

Variants and Related Words

• Conditional Probability: The most common and precise synonym for "contingent probability."
• Posterior Probability: A related term often used in Bayesian inference, referring to the updated probability of an event after considering new evidence.

Synonyms

• Conditional likelihood
• Dependent probability

Related Phrases

• "Given that...": A phrase commonly used when stating the condition in a contingent probability scenario.
  • We need the probability of success, given that the initial phase is completed.

Notes

• Key Distinction: Contingent probability is not the same as the joint probability (probability of two events occurring together) or the marginal probability (probability of a single event without conditions). It specifically requires a condition to be known.

Noun

1. the probability that an event will occur given that one or more other events have occurred